An overhead fold-up door, with height h and mass m, consists of two identical sections hin...

An overhead fold-up door, with height h and mass m, consists of two identical sections hinged at C. The roller at A moves along a horizontal guide, whereas the rollers at B and D, which are the midpoints of sections AC and CE, move along a vertical guide. The door’s operation is assisted by two identical springs attached to the horizontally moving rollers (only one of the two springs is shown). The springs are stretched an amount δ0 when the door is fully open.

Figure P7.80

Let h = 10 m and m = 320 kg. In addition, let k = 2400 N/m and δ0 = 0.15 m. Assuming that the door is released from rest when θ = 5°, determine the time the door will take to close and the speed of E at closing.